For reference, it's heavily indicated that the box is actually opened by XY: The big split appears to primarily be whether or not they have Mega Evolutions, which are tied to the events of the Kalos war and the firing of AZ's WMD.

Regarding character chronology, there is potential that Looker does have some continuity: He appears, hunting evil teams, then is somehow transported to the 'alt-world' with Megas, probably by being a Faller himself (given how his cameo in ORAS goes) and joins the police over there, but this time he's hunting Ultra Beasts. Personally I think there's going to be some link in the DP remakes where thee games return to the megaless world as their basis, the UBs appear and Looker disappears as a result. We may have gone full Zelda, but tbh there was very little synchronicity between games after the first two gens anyway.